数学
多稳态
四元数
指数稳定性
平衡点
分段
李雅普诺夫函数
人工神经网络
应用数学
功能(生物学)
非线性系统
理论(学习稳定性)
订单(交换)
不动点定理
控制理论(社会学)
纯数学
数学分析
计算机科学
微分方程
控制(管理)
财务
经济
人工智能
物理
机器学习
几何学
生物
进化生物学
量子力学
标识
DOI:10.1016/j.neucom.2021.03.079
摘要
In this paper, the multiple asymptotic stability is investigated for fractional-order quaternion-valued neural networks (FQVNNs) with time-varying delays. The activation function is a nonmonotonic piecewise nonlinear activation function. By applying the Hamilton rules, the FQVNNs are transformed into real-valued systems. Then, according to the Brouwer’s fixed point theorem, three new conditions are proposed to ensure that there exist 34n equilibrium points. Moreover, by virtue of fractional-order Razumikhin theorem and Lyapunov function, a new condition is derived to guarantee the FQVNNs have 24n locally asymptotic stable equilibrium points. For the first time, the multiple asymptotic stability of delayed FQVNNs is investigated. Contrast to multistability analysis of integer-order quaternion-valued neural networks, this paper present different conclusions. Finally, two numerical simulations demonstrate the validity of the results.
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